Abstract

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

@article{osti_1407880,
title = {Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions},
author = {Jin, Tao and Mourad, Hashem M. and Bronkhorst, Curt A. and Livescu, Veronica},
abstractNote = {Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.},
doi = {10.1007/s00466-017-1470-8},
journal = {Computational Mechanics},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 9
}

An explicit finite element formulation, used to study the behavior and failure mechanisms of metallic materials under high strain rate loading, is presented. The formulation is based on the assumed-strain approach of Fish and Belytschko [1988], which allows localization bands to be embedded within an element, thereby alleviating mesh sensitivity and reducing the required computational effort. The behavior of the material outside localization bands (and of the virgin material prior to the onset of strain localization) is represented using a Gurson-type coupled plasticity-damage model based on the work of Johnson and Addessio [1988]. Assuming adiabatic conditions, the response of themore » localization band material is represented by a set of constitutive equations for large elasticviscoplastic deformations in metals at high strain rates and high homologous temperatures (see Brown et al. [1989]). Computational results are compared to experimental data for different metallic alloys to illustrate the advantages of the proposed modeling strategy.« less

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

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